Poisson equation on complete manifolds

2017/01/11 by Ovidiu Munteanu, Munteanu, Ovidiu, Chiung-Jue Anna Sung +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1701.02865

openalex publication_date 2017/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci curvature bounded below. As an application, we show that the curvature of a steady gradient Ricci soliton must decay exponentially if it decays faster than linear and the potential function is bounded above.

Cited by

• Level set flow in 3D steady gradient Ricci solitons

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